Evaluate the definite integral. $\int^{0}_{1}\left(-9\sqrt{x}\right)\,dx = $
Solution: First, use the power rule: $\begin{aligned}\int^{0}_{1}\left(-9\sqrt{x}\right)\,dx ~&=~\int^{0}_{1}\left(-9x^{\frac12}\right)\,dx \\&=(-6x^\frac32)\Bigg|^{0}_{1}\end{aligned}$ Second, plug in the limits of integration: $(-6\cdot{0}^{\frac32})-(-6\cdot1^{\frac32}) = 0+6 = 6$. The answer: $\int^{0}_{1}\left(3\sqrt{x}\right)\,dx ~=~6$